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Sequentially Cohen-Macaulay monomial ideals of embedding dimension four · arXivDesk

math/0702569Feb 20, 200711 pages

Sequentially Cohen-Macaulay monomial ideals of embedding dimension four

Sarfraz Ahmad, Dorin Popescu

Commutative Algebra

Abstract

Let $I$ be a monomial ideal of the polynomial ring $S=K[x_1,...,x_4]$

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over a field

K

. Then

S/I

is sequentially Cohen-Macaulay if and only if

S/I

is pretty clean. In particular, if

S/I

is sequentially Cohen-Macaulay then

I

is a Stanley ideal.

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